Geometry Tips: General Tips For Geometric Proofs

1. Understand the problem. The most important step in proving something is realizing what is given, and what is  to be proven.

2. Understand the givens. You will always use what is given in the assumption. This would be the condition that comes after "If" or "Suppose" or
something along those lines.

3. Is there something that  you already know how to do that's related to the solution? You can use information that you already know, especially axioms or the results of other theorems.

4. Write out what is given, as well as what is needed to be proven. It shows that you will start with what is given, use other axioms, theorems, or math that you already know to be true, and arrive at what you want to prove. True understanding means you can repeat, and paraphrase the problem in at least
3 different ways: pure symbols, flowchart, and using words.

5. Ask yourself questions as you move along. "Why is this so?" and "Is there any way this can be false?" are good questions for every statement, or claim. These questions will be asked by your professor in every step, and as soon as he/she can't verify one of those questions, your grade will go down. Back up every statement with a reason! Justify your process.

6. Make sure your proof is step-by-step. It needs to flow from one statement to the other, with support for each statement, so that there is no reason to doubt the validity of your proof. It should be constructionist, like building a house: orderly, systematic, and with properly paced progress.
7. Ask your professor or classmate if you have questions. Stand on the shoulders of giants, but do not be a thief.










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